1. Technical Field of the Invention
This invention relates generally to an analog circuit, and more particularly, to an analog circuit approach to implement a continuous wavelet transform circuit to decompose an input signal using a wavelet basis to produce a time-frequency description of the input signal.
2. Description of the Related Art
Decomposition of a signal into components with respect to frequency and time was studied in the past. Prior works were related to the orthogonal decomposition of a signal where time and frequency were unrelated to one another. This decomposition is called as xe2x80x9cwavelet transformxe2x80x9d which is dependent both on frequency and time.
Various analog and switched-capacitor continuous wavelet transform circuits have been proposed for audio frequency operation. High frequency continuous wavelet transform circuits have potential applications in radar and communications signals processing. Radar applications for wavelet decomposition include chirp detection and matched filtering since radar returns are attenuated, delayed, and dilated versions of transmitted radar pulses.
U.S. Pat. No. 4,974,187 to Lawton discloses a system that decomposes a digital input sequence into its digital wavelet transform. The digital sampling of an analog input to form the digital input sequence loses some of the information of the input signal.
U.S. Pat. No. 5,495,554 to Edwards et al. discloses an analog wavelet transform circuitry for implementing a continuous wavelet transform by forming a multiplicity of analog wavelet outputs. The method comprises filtering an input signal to produce a multiplicity of analog wavelet outputs; sampling the multiplicity of analog wavelet outputs to produce digitally sampled wavelet data; and compressing the digitally sampled wavelet data into a reduced amount of digital data.
Also, wavelet transforms have been suggested in the prior art for use in data compression wherein signal information is arranged in a fashion that would facilitate data compression. Thus, wavelet transforms have many applications in signal processing and image processing. Usually, wavelet transforms are used on discrete-time digital data. However, for certain applications, the wavelet decomposition cannot be performed in real-time using conventional sampled-data and digital techniques. The prior art references fail to teach or suggest an analog continuous wavelet transform circuit which provides a real-time wavelet decomposition at high sampling frequencies. Furthermore, none of the prior art references teach or suggest an analog wavelet transform circuit wherein increasing the number of channels (i.e., the size of the filter bank) does not increase the time required to perform the wavelet decomposition.
Thus, there is a need for an analog continuous wavelet transform circuit which provides a real-time wavelet decomposition at high sampling frequencies. There is also a further need for an analog continuous wavelet transform circuit wherein increasing the number of channels (i.e., the size of the filter bank) does not increase the time required to perform the wavelet decomposition. The system and method of the present invention offers an effective solution overcoming the problems encountered by the prior art.
Accordingly, the present invention is directed to an analog continuous wavelet transform circuit and method for decomposing an input signal using a wavelet basis to produce a time-frequency description of the input signal.
In one aspect, the present invention is directed to an analog continuous wavelet transform apparatus which comprises a plurality of quadrature voltage controlled oscillators (VCOs) for generating center frequencies of a plurality of synchronous receivers, wherein each quadrature VCO generates differential in-phase (I) and quadrature (Q) outputs. The plurality of synchronous receivers act as a bandpass filter bank which comprises a plurality of bandpass filters. The center frequency of each of the plurality of bandpass filters is set by the frequency of a corresponding voltage controlled oscillator, and bandwidth of each of the bandpass filters is set by bandwidth of a lowpass filter of a corresponding synchronous receiver. The bandwidths of each of the bandpass filters is chosen in such a manner so as to make the overall power response of the bank of bandpass filters uniform over the frequency range of the bandpass filter bank.
Each of the synchronous receivers of the analog continuous wavelet transform apparatus further comprises at least one multiplier, at least one gain amplifier, and at least one squarer for both in-phase (I) and quadrature (Q) phase to produce a squarer output, and means for combining the squarer outputs to produce a synchronous receiver output. Gilbert multipliers may be used to perform the multiplication and squaring functions. The wavelet transform apparatus further includes a circuit to remove the offset of the gain amplifier. The output of each of the synchronous receivers represents the instantaneous input signal power within a specific bandpass filter. Each of the bandpass filters may act as a channelized receiver. Each squarer further comprises at least one adder circuit, and an analog compressing circuit implemented within the adder circuit in order to increase the dynamic range of the wavelet transform apparatus.
The order of each of the bandpass filters is determined by the order of a corresponding synchronous, receiver. Resistive dividers may be used to bias the intermediate VCOs among the plurality of the VCOs. The endpoints of the resistor dividers may be biased using fixed voltages or by using phase locked loops (PLLs) having fixed frequency reference as inputs. The voltages to the resistor voltage dividers are controlled by applying programmable voltages. The wavelet transform apparatus further includes analog-to-digital converters for converting the analog output to a digital output for each of the bandpass filters. An analog multiplexer may be used for multiplexing a plurality of parallel bandpass filter outputs to a single analog-to-digital converter. The wavelet transform apparatus further comprises a plurality of frequency synthesizers to generate the center frequencies of the plurality of synchronous receivers. The plurality of frequency synthesizers are implemented with at least one of PLL architecture, fractional-N PLL architecture, or direct digital synthesizer (DDS) architecture.
In another aspect, the present invention is directed to a method for performing time-frequency decomposition of a high frequency input signal using a wavelet basis, comprising generating differential in-phase (I) and quadrature (Q) outputs by a plurality of quadrature voltage: controlled oscillators (VCOs). The high frequency input signal is filtered by means of a plurality of synchronous receivers acting as a bandpass filter bank. Each of the synchronous receivers act as a bandpass filter, and the center frequency of each of the synchronous receivers is set by a frequency of a corresponding voltage controlled oscillator (VCO). An output is produced at each of the synchronous detectors wherein each of the outputs represents an instantaneous input signal power within a corresponding bandpass filter.
In another exemplary embodiment, the high frequency input signal is a one-dimensional time signal having a time-varying voltage. The bandpass filter bank measures the energy of the input signal within an overlapping bank of bandpass filters. Further, the simultaneous sampling of outputs of each of the bandpass filters is performed using sample-and-hold circuits.
Still other objects and advantages of the present invention will become apparent to those skilled in the art from the following detailed description, wherein only the preferred embodiment of the invention is shown and described, simply by way of illustration of the best mode contemplated of carrying out the invention. As will be realized, the invention is capable of different embodiments, and its several details are capable of modifications in various obvious respects, all without departing from the invention. Accordingly, the drawings and description are to be regarded as illustrative in nature, and not as restrictive.